Perovskite solar cells have emerged as a promising photovoltaic technology due to their rapidly advancing power conversion efficiency, which has now surpassed 26%. However, the majority of high-performance perovskite solar cells rely on lead-based compounds such as CH3NH3PbI3 (MAPbI3) and FAPbI3, raising environmental and health concerns. The pursuit of green and sustainable energy solutions necessitates the reduction or elimination of lead in perovskite solar cells while maintaining high efficiency and stability. In this study, we explore the potential of germanium-based perovskite materials, specifically n-type and p-type methylammonium germanium iodide (n-MAGeI3 and p-MAGeI3), to form a homojunction structure as the light-absorbing layer. This design aims to enhance carrier dissociation and transport, addressing key challenges in lead-free perovskite solar cells.
We employ the SCAPS-1D simulation software to investigate the optoelectronic properties of the proposed device structure. The software solves fundamental equations governing semiconductor behavior, including the Poisson equation and continuity equations for electrons and holes. The Poisson equation is given by:
$$ -\frac{\partial}{\partial x} \left( -\varepsilon(x) \frac{\partial V}{\partial x} \right) = q \left[ p(x) – n(x) + N_D^+(x) – N_A^-(x) + p_t(x) – n_t(x) \right] $$
where \( \varepsilon \) is the dielectric constant, \( V \) is the electrostatic potential, \( q \) is the elementary charge, \( p \) and \( n \) are the hole and electron concentrations, \( N_D^+ \) and \( N_A^- \) are ionized donor and acceptor densities, and \( p_t \) and \( n_t \) are trapped hole and electron densities. The continuity equations for holes and electrons are expressed as:
$$ \frac{\partial p}{\partial t} = \frac{1}{q} \frac{\partial J_p}{\partial x} + G_p – R_p $$
$$ \frac{\partial n}{\partial t} = \frac{1}{q} \frac{\partial J_n}{\partial x} + G_n – R_n $$
Here, \( J_p \) and \( J_n \) represent the hole and current densities, \( G_p \) and \( G_n \) are the generation rates, and \( R_p \) and \( R_n \) are the recombination rates for holes and electrons, respectively. These equations form the basis for simulating the performance of perovskite solar cells under AM 1.5G illumination.
In our device design, we propose a structure comprising fluorine-doped tin oxide (FTO) as the transparent conductive oxide, Cd0.5Zn0.5S as the electron transport layer (ETL), an n-MAGeI3/p-MAGeI3 homojunction as the perovskite absorber, MASnBr3 as the hole transport layer (HTL), and platinum (Pt) as the back contact. This configuration is compared to conventional structures using TiO2 as the ETL and Spiro-OMeTAD as the HTL to highlight the advantages of our approach. The key material parameters used in the simulation are summarized in Table 1.
| Material | Bandgap (Eg, eV) | Electron Affinity (χ, eV) | Dielectric Permittivity (εr) | NC (cm⁻³) | NV (cm⁻³) | μn (cm²/V·s) | μp (cm²/V·s) | ND (cm⁻³) | NA (cm⁻³) | Defect Density (cm⁻³) | Thickness (nm) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Cd0.5Zn0.5S (ETL) | 2.8 | 3.8 | 10 | 1e18 | 1e18 | 100 | 25 | 1e17 | 0 | 1e14 | 200 |
| n-MAGeI3 | 1.9 | 3.98 | 10 | 1e16 | 1e15 | 162 | 101 | 1e15 | 0 | 1e14 | 480 |
| p-MAGeI3 | 1.9 | 3.98 | 10 | 1e16 | 1e15 | 162 | 101 | 0 | 1e17 | 1e14 | 60 |
| MASnBr3 (HTL) | 2.15 | 3.39 | 8.2 | 1e18 | 1e18 | 1.6 | 1.6 | 0 | 1e18 | 1e14 | 200 |
| TiO2 (ETL) | 3.2 | 4 | 19 | 2e18 | 2e19 | 0.2 | 0.1 | 3e19 | 0 | 1e14 | 200 |
| MAGeI3 (single) | 1.9 | 3.98 | 10 | 1e16 | 1e16 | 1.62e5 | 1.01e5 | 1e9 | 1e9 | 1e14 | 540 |
| Spiro-OMeTAD (HTL) | 3 | 2.45 | 3 | 2.2e18 | 1.9e19 | 2e-4 | 2e-4 | 0 | 1e18 | 1e14 | 200 |
| FTO | 3.5 | 4 | 9 | 2.2e18 | 1.8e19 | 20 | 10 | 1e19 | 0 | 1e14 | 50 |
The initial simulation results demonstrate that the homojunction structure significantly improves the performance of perovskite solar cells compared to single-layer absorbers. The current-density voltage (J-V) characteristics under AM 1.5G illumination show that the device with n-MAGeI3/p-MAGeI3 homojunction achieves a higher open-circuit voltage (VOC), short-circuit current density (JSC), and fill factor (FF) than the reference structures. The quantum efficiency (QE) analysis further reveals that the homojunction design enhances light absorption and carrier collection across a broad wavelength range. The built-in potential (Vbi) of the homojunction device is calculated to be 1.591 eV, which is higher than that of the single-layer perovskite solar cells, contributing to the improved VOC. The relationship between Vbi and VOC can be approximated by:
$$ V_{OC} \approx \frac{kT}{q} \ln \left( \frac{J_{SC}}{J_0} + 1 \right) $$
where \( k \) is Boltzmann’s constant, \( T \) is temperature, and \( J_0 \) is the reverse saturation current density. The enhanced Vbi in the homojunction structure reduces carrier recombination and facilitates efficient charge extraction.
To optimize the device performance, we investigate the impact of ETL and HTL thicknesses on the photovoltaic parameters. The thickness of the Cd0.5Zn0.5S ETL is varied from 50 nm to 500 nm while keeping the MASnBr3 HTL thickness constant at 200 nm. Similarly, the HTL thickness is varied from 50 nm to 500 nm with a fixed ETL thickness of 200 nm. The results indicate that the HTL thickness has a more pronounced effect on the device performance than the ETL thickness. This is attributed to the dual role of MASnBr3 as both a hole transporter and a supplementary light absorber. The absorption of photons in the HTL layer is described by the Lambert-Beer law:
$$ S(\lambda) = S_0(\lambda) \exp \left( -\sum_{i=1}^{4} \alpha_{\text{mat}_i} d_{\text{mat}_i} \right) $$
where \( S_0(\lambda) \) is the incident light intensity, \( S(\lambda) \) is the transmitted intensity, \( \alpha_{\text{mat}_i} \) is the absorption coefficient of each layer, and \( d_{\text{mat}_i} \) is the thickness of the respective layer. The optimal HTL thickness is found to be 500 nm, which allows complete absorption of photons in the 520-577 nm range that are not absorbed by the perovskite layer. The photovoltaic parameters for different ETL and HTL thicknesses are summarized in Table 2 and Table 3.
| ETL Thickness (nm) | VOC (V) | JSC (mA/cm²) | FF (%) | PCE (%) |
|---|---|---|---|---|
| 50 | 1.9064 | 14.9842 | 88.69 | 25.33 |
| 100 | 1.9065 | 14.9853 | 88.69 | 25.34 |
| 200 | 1.9066 | 14.9867 | 88.69 | 25.34 |
| 300 | 1.9066 | 14.9871 | 88.69 | 25.34 |
| 400 | 1.9066 | 14.9867 | 88.69 | 25.34 |
| 500 | 1.9065 | 14.9854 | 88.69 | 25.34 |
| HTL Thickness (nm) | VOC (V) | JSC (mA/cm²) | FF (%) | PCE (%) |
|---|---|---|---|---|
| 50 | 1.9062 | 14.8222 | 88.69 | 25.06 |
| 100 | 1.9063 | 14.8878 | 88.69 | 25.17 |
| 200 | 1.9066 | 14.9867 | 88.69 | 25.34 |
| 300 | 1.9067 | 15.0553 | 88.69 | 25.46 |
| 400 | 1.9068 | 15.1038 | 88.69 | 25.54 |
| 500 | 1.9069 | 15.1388 | 88.69 | 25.60 |
Another critical factor influencing the performance of perovskite solar cells is the defect density in the absorber layer. We analyze the effect of varying defect densities in the n-MAGeI3 and p-MAGeI3 layers on the device parameters. When the defect density in p-MAGeI3 is fixed at 10¹⁴ cm⁻³, reducing the defect density in n-MAGeI3 from 10¹⁸ cm⁻³ to 10¹⁰ cm⁻³ leads to a significant improvement in PCE from 16.30% to 27.15%. Similarly, when n-MAGeI3 defect density is fixed at 10¹⁴ cm⁻³, varying p-MAGeI3 defect density from 10¹⁸ cm⁻³ to 10¹⁰ cm⁻³ increases PCE from 20.69% to 25.66%. The results indicate that the n-MAGeI3 layer has a more substantial impact on device performance due to its higher exposure to incident light and greater involvement in carrier generation and recombination. The defect-assisted recombination rate can be expressed as:
$$ R = \frac{np – n_i^2}{\tau_p (n + n_t) + \tau_n (p + p_t)} $$
where \( n_i \) is the intrinsic carrier concentration, \( \tau_n \) and \( \tau_p \) are the electron and hole lifetimes, and \( n_t \) and \( p_t \) are the trap densities. Lower defect densities reduce recombination losses, thereby enhancing the overall efficiency of the perovskite solar cell.
The energy band diagram of the optimized device reveals the alignment of energy levels at the interfaces, which facilitates efficient charge transport. The use of Cd0.5Zn0.5S as the ETL provides a better energy level match with the perovskite layer compared to TiO2, reducing interface recombination. Similarly, MASnBr3 as the HTL not only transports holes but also absorbs high-energy photons, generating additional electron-hole pairs. The homojunction structure creates an internal electric field that promotes the separation of photogenerated carriers, as described by the drift-diffusion model:
$$ J_n = q \mu_n n E + q D_n \frac{dn}{dx} $$
$$ J_p = q \mu_p p E – q D_p \frac{dp}{dx} $$
where \( E \) is the electric field, \( \mu_n \) and \( \mu_p \) are the electron and hole mobilities, and \( D_n \) and \( D_p \) are the diffusion coefficients. The homojunction enhances the drift component of the current, leading to higher collection efficiency.
After thorough optimization of the layer thicknesses and defect densities, the best-performing perovskite solar cell achieves a VOC of 1.9069 V, JSC of 15.1388 mA/cm², FF of 88.69%, and PCE of 25.60%. This represents a significant improvement over the reference devices with TiO2/Spiro-OMeTAD (PCE = 23.47%) and Cd0.5Zn0.5S/MAGeI3/MASnBr3 (PCE = 25.33%). The enhanced performance is attributed to the synergistic effects of the homojunction absorber, optimized charge transport layers, and reduced defect densities. The results underscore the potential of germanium-based perovskite materials in developing high-efficiency, lead-free perovskite solar cells.
In conclusion, our simulation study demonstrates that the n-MAGeI3/p-MAGeI3 homojunction structure, combined with Cd0.5Zn0.5S ETL and MASnBr3 HTL, offers a viable pathway for achieving high-performance perovskite solar cells without lead. The homojunction design improves carrier dissociation and transport, while the optimized thicknesses and defect densities minimize losses. Future work should focus on experimental validation and further refinement of material parameters to realize the full potential of this approach in practical applications. The continuous advancement in perovskite solar cell technology will benefit from such innovative designs that prioritize both efficiency and environmental sustainability.